Download Hipparcos distance estimates of the Ophiuchus and the Lupus cloud

Astronomy
&
Astrophysics
A&A 480, 785–792 (2008)
DOI: 10.1051/0004-6361:20079110
c ESO 2008
Hipparcos distance estimates of the Ophiuchus
and the Lupus cloud complexes
M. Lombardi1,2 , C. J. Lada3 , and J. Alves4
1
2
3
4
Space Telescope European Coordination Facility/ESO, Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
e-mail: [email protected]
University of Milan, Department of Physics, via Celoria 16, 20133 Milan, Italy (on leave)
Harvard-Smithsonian Center for Astrophysics, Mail Stop 42, 60 Garden Street, Cambridge, MA 02138, USA
Calar Alto Observatory – Centro Astronómico Hispano Alemán, C/Jesús Durbán Remón 2-2, 04004 Almeria, Spain
Received 20 November 2007 / Accepted 16 January 2008
ABSTRACT
We combine extinction maps from the Two Micron All Sky Survey (2MASS) with Hipparcos and Tycho parallaxes to obtain reliable
and high-precision estimates of the distance to the Ophiuchus and Lupus dark complexes. Our analysis, based on a rigorous maximumlikelihood approach, shows that the ρ-Ophiuchi cloud is located at (119 ± 6) pc and the Lupus complex is located at (155 ± 8) pc;
in addition, we are able to put constraints on the thickness of the clouds and on their orientation on the sky (both these effects are
not included in the error estimate quoted above). For Ophiuchus, we find some evidence that the streamers are closer to us than the
core. The method applied in this paper is currently limited to nearby molecular clouds, but it will find many natural applications in
the GAIA-era, when it will be possible to pin down the distance and three-dimensional structure of virtually every molecular cloud in
the Galaxy.
Key words. ISM: clouds – dust, extinction – ISM: individual objects: Ophiuchus complex – stars: distances – methods: data analysis
1. Introduction
In recent years, much effort has been dedicated to the study of
dark molecular clouds and their dense cores. One of the main
motivations for these investigations is the study of the process
of star and planet formation in its entirety, and a deeper understanding of the effects of the local environment. A key aspect of the scientific analysis of a dark molecular cloud is its
distance, which is related to many physically relevant properties (in particular, the mass scales as the square of the distance).
Unfortunately, the distance estimates for many clouds are often
plagued by very large uncertainties and it is not rare to see in
the literature measurements that differ by large factors. Often,
this quantity is inferred by associating the cloud to other astronomical objects whose distance is well known. For example, the Lupus complex is located near the Sco OB2 association (Humphreys 1978; de Zeeuw et al. 1999), whose distance
is estimated to be ∼150 pc based on the photometry of OB stars
(Krauuter 1991). However, this method is based on some degree
of arbitrariness when making the link between the cloud and the
other objects, and thus the deduced distance can be completely
unreliable.
The cloud complexes considered in this paper, the ρ
Ophiuchi and the Lupus dark clouds, are good examples of
how different distance estimates made by different authors can
be. Quoted values for the ρ-Ophiuchi cloud are in the range
120–165 pc, as recently summarized by Rebull et al. (2004).
Chini (1981) estimated the distance to be ∼160 pc from multicolor photometry of heavily absorbed stars in the ρ Oph core,
while Knude & Hog (1998) suggested a significantly smaller
figure, ∼120 pc. For Lupus, the situation is even more extreme,
with estimates from 100 pc (Knude & Hog 1998) to 190 pc
(Wichmann et al. 1998), both based on Hipparcos data; the most
widely accepted distance is in the middle of these two extremes,
at approximately 140 pc (Hughes et al. 1993; de Zeeuw et al.
1999).
These uncertainties severely hamper our understanding of
the physical properties of molecular clouds, and thus our knowledge of star formation. For example, an error by a factor two on
the distance of a cloud translates into an error by a factor four
in the mass, and has a thus a huge impact on the estimate of
the density, size, stability, and star formation efficiency of their
cloud cores (see Alves et al. 2007, for further discussions on this
point).
In this paper we present accurate distance measurements of
the Ophiuchus and Lupus complexes based upon Hipparcos and
Tycho parallaxes. Our technique is statistically sound and, when
applied to nearby giant molecular clouds, is able to provide accurate distance measurements and related errors. The paper is organized as follows. In Sect. 2 we present the main datasets used
and discuss a simple approach to the problem. A more quantitative technique is developed in Sect. 3, where we also presents the
results obtained for the two clouds considered in this paper. The
technique is further developed in Sect. 4 to include the effects of
the cloud thickness and orientation. Finally, in Sect. 5 we briefly
discuss the results obtained.
2. Basic analysis
Our technique is based on a simple fact: stars observed through
high column-densities must exhibit a significant reddening,
while foreground stars will show no reddening even when observed in projection toward dense regions of the cloud. The first
step was thus to make reliable extinction maps of the ρ-Ophiuchi
Article published by EDP Sciences
786
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
1.0
0.8
0.6
AK
Galactic Latitude
20°
15°
0.4
0.2
10°
0.0
5°
0°
355°
350°
Galactic Longitude
Fig. 1. The Ophiuchus region considered. The gray map shows 2MASS/Nicer extinction, with overlaid the AK = 0.1 mag (smoothed) contour.
The dots indicate the position of the Hipparcos stars used for the analysis. The boxed area indicates the central part of the cloud.
and Lupus clouds in order to delineate the cloud boundaries
and regions to be considered for the distance analysis. For the
purpose, we used approximately 42 million stars from the Two
Micron All Sky Survey (2MASS) point source catalog to construct a 1672 square degrees Nicer (Lombardi & Alves 2001)
extinction map of the Ophiuchus and Lupus dark nebulæ. The
map, described elsewhere (Lombardi et al. 2008), has a resolution of 3 arcmin and a 3σ detection level of 0.5 visual magnitudes. We considered the two regions shown in Figs. 1 and 2,
approximately corresponding to the galactic coordinates
− 12◦ < l < 2◦
9◦ < b < 24◦
(1)
for Ophiuchus, and
353◦ < l < 345◦
4◦ < b < 19◦
(2)
for Lupus, and selected there all Hipparcos and Tycho (Perryman
et al. 1997) parallax measurements of stars in regions characterized by a relatively high column densities (more precisely,
in regions with AK > 0.1 mag in our 2MASS extinction
map). Finally, in order to estimate the intrinsic colors of the
Hipparcos stars, we obtained their spectral types. For the purpose, we used the All-Sky Compiled Catalogue (ASCC-2.5;
Kharchenko 2001), which lists 2 501 304 stars taken from several sources (mainly the Hipparcos-Tycho family, the groundbased Position and Proper Motion family, and the Carlsberg
Meridian Catalogs), and the “Tycho-2 Spectra Type Catalog”
(Tycho-2spec, III/231; Wright et al. 2003), which crossreferences 351 863 Tycho stars with spectral catalogues (mainly
the Michigan catalogs). In summary, our joined catalog contains
for each star observed in projection with relatively large extinction regions the parallax and its related error, the spectral type,
and a set of visual magnitudes with errors.
We then considered all Hipparcos stars with well determined
parallaxes (we required the parallax error to be smaller than
3 mas) in the region considered, and estimated the intrinsic B−V
of each star from its spectral type (for this purpose, we used the
color tables in Landolt-Börnstein 1982, p. 15, and the normal
reddening law of Rieke & Lebofsky 1985). Finally, we evaluated the extinction of each star by comparing its observed B − V
color with its estimated intrinsic color. As final selection, we
required stars to have a V-band extinction error smaller than
1 mag, which left 180 objects in the Ophiuchus region, and 186
objects in the Lupus region. A plot of the star column density
versus the Hipparcos parallax for both cloud complexes is shown
in Figs. 3 and 5; a distance-reddening zoom plot for Ophiuchus
is presented in Fig. 4.
Figure 3 proves the effectiveness of the parallax method:
from the right to the left, stars are initially found close to the
AV = 0 mag line, with a relatively low dispersion; then, as we go
to smaller parallaxes, an impressive “wall” of stars with significant reddening is observed (approximately at π = 8 mas). Since
for Fig. 3 we only selected stars observed against high-column
density regions in Ophiuchus, and we further excluded stars
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
787
1.0
20°
0.8
15°
AK
Galactic Latitude
0.6
0.4
10°
0.2
5°
0.0
345°
340°
Galactic Longitude
335°
Fig. 2. Same as Fig. 1, but for Lupus.
with suboptimal measurement errors, the parallax-reddening
plot appears extremely clear and gives alone an accurate measurements of the distance of the cloud, that we estimate to be
approximately 120 pc.
The same plot for the Lupus region, shown in Fig. 5, appears
to be slightly less clear, for several reasons. First, Lupus has a
complex structure and is composed of several subclouds spanning several degrees (see Fig. 2); hence, it is not unlikely that
different clouds are located at different distances (see discussion
below). In addition, the Lupus cloud complex seems to be at
a larger distance than Ophiuchus, at the limit of the Hipparcos
sensitivity, and hence the plot of Fig. 5 is perhaps not as crystal
clear as the one of Fig. 3. Still, a preliminary qualitative analysis
indicates a cloud distance close to 150 pc for Lupus.
An intrinsic problem of this technique is that, in this basic
formulation, it does not allow a simple, robust estimate of the
788
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
∞
3
200
100
Distance (pc)
70
50
40
∞
3
35
Distance (pc)
70
100
50
40
35
2
AV (mag)
AV (mag)
2
200
1
0
1
0
-1
-1
0
10
20
30
0
10
20
Parallax (mas)
30
Parallax (mas)
Fig. 3. The reddening of Hipparcos and Tycho stars observed in direction of high integrated column densities (AK > 0.1 mag) in the
Ophiuchus field. Only stars with relative error on the parallax smaller
than 0.3 were plotted here. In this and other plots the reddening has
been converted into V-band extinction by assuming a normal reddening
law (Rieke & Lebofsky 1985).
3
Fig. 5. The reddening of stars as a function of their parallaxes in the
Lupus region (filled circles: AV > 1.5 mag; open circles: AV > 1 mag).
Stars with relative parallax error larger than 0.5 were excluded from
this plot. If the cloud were a perfect “wall” of dust, we would obtain a
Heaviside function with the discontinuity at the parallax of the cloud,
much like Fig. 3 for Ophiuchus. Measurement errors, the complex structure of the cloud, and the small number statistics all make this plot to
more scattered and thus less clear.
variance. Mathematically, we considered the two distributions
fg
p (AV ) =
bg
AV (mag)
fg2
pfg (AV ) = Gau(AV |AV , σAV + σ2AV ),
2
bg
bg2
Gau(AV |AV , σAV
+
(3)
σ2AV ),
(4)
where we denoted with Gau(x| x̄, σ2x ) the value at x of a normal probability density with mean x̄ and variance σ2x . The two
distributions pfg and pbg refers to foreground (i.e., almost unextincted) and background (heavily extincted) stars. These are
taken to be normal distributions with variances given by the sum
fg2
bg2
of the intrinsic scatter of column densities (σAV and σAV ) and
2
of the measurement error for the star considered (σAV ). Note, in
1
0
-1
bg
300
particular, that σAV accounts for the local changes in the cloud
Fig. 4. The reddening as a function of the Tycho distance for Ophiuchus
stars. The plot shows the same points as Fig. 3, but is done in distance instead of in parallaxes (and, as a result, error bars in distance
are approximated). Filled dots are stars for which the local extinction is
AK > 0.15 mag, open dots stars with AK > 0.1 mag. This figure can be
better used to obtain a precise distance of the cloud, that we evaluate as
d = (120 ± 10) pc.
column density with respect to the average value AV , while σAV
is introduced to allow for underestimates of the photometric errors on the star magnitudes or for foreground, thin nearby clouds.
Finally, the probability distribution p(AV |π) for the AV measurement for a star at parallax π was taken to be
⎧ fg
⎪
if π > πcloud ,
⎪
⎨ p (AV )
(5)
p(AV |π) = ⎪
⎪
fg
bg
⎩ (1 − f )p (AV ) + f p (AV ) if π ≤ πcloud .
error associated with the distance measurement. In addition, the
value provided must be regarded as an upper limit, since the distance is typically estimated from the first star that shows a significant reddening.
Note that the parameter f ∈ [0, 1] denotes the “filling factor”, i.e.
the probability that a background star is extincted by the cloud.
this simple
model leaving all parameters
We considered
fg
fg
bg
bg
πcloud , f, AV , σAV , AV , σAV free. In order to assess the goodness
of a model, we computed the likelihood function, defined as
0
100
200
Distance (pc)
3. Likelihood analysis
A less qualitative estimate can be obtained by using a statistical
model for the parallax-reddening relation. Following Lombardi
et al. (2006), we assumed that the AV measurement for foreground stars is small, while a fraction f of the background stars
is distributed as a normal variable with relative large mean and
bg
fg
fg
n=1
0
bg
fg
bg
L(πcloud , f, AV , σAV , AV , σAV )
N ∞ (n) (n) (n) π p π π̂ dπ,
p A(n)
V
(6)
where the product
over all N stars of Figs. 3 and 5,
is carried
and where p π(n) π̂(n) is the probability distribution that the
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
where σ̂(n)
π is the estimated error on the parallax. Note that the
use of normal distributions in Eqs. (3), (4), and (7) makes it possible to perform the integral (6) analytically in terms of the error
function erf.
The likelihood function (6) was analysed using Monte Carlo
Markov Chains (MCMC; see, e.g. Tanner 1991). Figure 6 shows
the likelihood as a function of the cloud distance, marginalized with respect to all other parameters. From this figure we
can trivially evaluate the confidence regions for the estimated
distances; in particular, we obtain dOph = (119 ± 6) pc, and
dLup = (155 ± 8) pc, both at the 68% confidence level (since the
likelihood function is well approximated by a Gaussian, other
confidence bounds can easily derived from the errors quoted
here). We stress that the errors quoted here include only statistical errors, as deduced from the parallaxes and reddening uncertainties; other effects, such as the thickness of the cloud or its orientation in the sky are not taken into account and are discussed
below in Sect. 4. We stress also that the Lupus distance estimate
approximately refers to the average location of background stars
in the field (i.e., to l = 339◦ and b = 7◦ ), approximately 5.5 degrees south than the center of the field considered, and that only
a few stars are observed through Lupus 1. This difference can
play a significant role in case of noticeable tilts in the cloud orientation or in case of multiple components at different distances
(see below).
Note that the reliability of the maximum-likelihood technique presented here was also checked with numerical simulations. It is well known that the maximum-likelihood method
is, under certain circumstances (verified in our case), asymptotically unbiased; however, we decided to test its behaviour in our
specific case, with a limited (although large) number of data.
For the purpose, we simulated a “thin” cloud together with observation of a population of stars. We included reasonable errors
on both the star parallaxes and column densities, and recovered
the distance of the cloud using the same method described here.
These simulations confirmed that our estimate is essentially unbiased (i.e., that on average it returns the true distance of the
cloud), and that the error provided is reliable.
We also considered a two-screen configuration, with two partially overlapping clouds at different distances, and checked the
distance provided by the method. Interestingly, the simulation
showed that in this case the method tends to return a “weighted”
distance, i.e. a weighted mean of distance of the two screens
(where the weights are essentially proportional to the number of
stars intercepted by the two screens and by the column densities
associated with the two clouds). This result is very encouraging,
since it guarantees that, at least in the relatively simple cases
considered, the maximum likelihood provide a sensible and unbiased estimate of the cloud distance. Note, however, that the last
result also shows that in case of composite clouds with significantly different densities of background stars (e.g., because of
their different galactic latitude), the maximum-likelihood technique will be biased toward the distance of the cloud with the
highest density of stars. This point is particularly relevant for
Lupus, a cloud complex that spans several degrees in galactic
latitude, and for which there are indications of possible different
∞
0.12
200
Distance (pc)
100
70
0.10
0.08
Likelihood
nth star with measured parallax π̂(n) has a true parallax π(n) . Note
that the integral appearing in Eq. (6) properly takes into account
the possibility that a star with a measured parallax π̂(n) < πcloud
(or π̂(n) > πcloud ) is incorrectly taken as background (respectively,
foreground). For this probability we used a normal distribution:
p π̂(n) π(n) = Gau π̂(n) π(n) , σ̂(n)2
,
(7)
π
789
0.06
0.04
0.02
0.00
0
5
10
15
Parallax (mas)
Fig. 6. The likelihood function of Eq. (6) for Lupus (left black histogram) and Ophiuchus (right black histogram) as a function of the
cloud parallax πcloud marginalized over all the other parameters. Both
histograms shows marked peaks at πLup 7 mas and πOph 9 mas,
corresponding to distances of approximately 119 pc and 155 pc, respectively. The grey histogram refers to the likelihood function for the central region of Ophiuchus (marked window in Fig. 1).
distances among the various subclouds (see below Sect. 4.2; cf.
also Alves & Franco 2006).
4. Second order geometrical effects
Given the angular size of the regions considered, it is not unlikely that the cloud complexes have a thickness of 15 pc or
more. Similarly, even for “thin” clouds, we can easily imagine that they are not perfectly perpendicular to the line of sight
and that different regions of them are at different distances. All
these geometrical effects can be introduced in the maximumlikelihood analysis discussed above.
4.1. Cloud thickness
The thickness of a molecular cloud can be investigated by modifying the probability distribution of Eq. (5). This can be done
in several ways, which corresponds to different “definitions” of
the thickness of a cloud. We chose to parametrize the thickness
as a continuous, linear transition in the filling factor f , which
effectively becomes a function of the parallax. Hence, we wrote
p(AV |π) = f (π)pbg (AV ) + 1 − f (π) pfg (AV ),
(8)
where
⎧
⎪
0
if π > π1 ,
⎪
⎪
⎪
⎪
⎨
fmax (π − π1 )/(π2 − π1 ) if π2 < π < π1 .
f (π) = ⎪
⎪
⎪
⎪
⎪
⎩ fmax
if π < π2 .
(9)
In other words, stars up to the lower distance of the cloud
(π > π1 ) show no extinction, and thus their column density is
distributed according to pfg (AV ); similarly, stars background to
the cloud (π < π2 ) follow, with probability fmax (the usual filling factor), a distribution pbg (AV ); finally, stars embedded in the
cloud (π2 < π < π1 ) present an effective filling factors that raises
linearly within the cloud from 0 to fmax . Clearly, both parallaxes
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
200
200
150
150
Thickness (pc)
Thickness (pc)
790
100
50
50
0
80
100
120
140
Distance (pc)
160
100
Fig. 7. A density plot of the likelihood of Eq. (6) with for Ophiuchus
with the extinction probability distribution (8), as a function of the cloud
distance and thickness (the likelihood has been marginalized with respect to all other parameters). The three curves enclose regions of 68%,
95%, and 99.7% confidence level, while the line-filled corner in the topleft indicate a region that is physically excluded (observer embedded
in the cloud). The two plots at the top and at the right show the distance and thickness marginalized probabilities, together with the median value (solid line) and the usual three confidence regions (dashed
and dotted lines).
π1 and π2 were taken as free parameters. Note that, similarly to
Eq. (5), the use of a simple linear function for f (π) guarantees
that we can express analytically the integral of Eq. (6).
The results of a MCMC analysis of the likelihood function (6) with the distribution of Eq. (8) are shown in Fig. 7
for Ophiuchus and in Fig. 8 for Lupus. The plots in these figures indicate that, unfortunately, the quality and quantity of the
available parallaxes is not sufficient to put strong constraints on
the thickness of the clouds. In particular, for Ophiuchus we obtained a median thickness of 28+29
−19 pc, but the errors are clearly
very large; the situation is even more extreme for Lupus, with
a thickness estimate of 51+61
−35 pc. Still, this analysis is important
because it can in principle provide different distributions for the
distances of the two clouds (see top plots in Figs. 7 and 8) with
respect to the ones obtained from the simpler analysis of Sect. 3
(Fig. 6). In this respect, the fact that the two results obtained
are almost identical confirms the robustness of our distance estimates. In addition, the much larger thickness estimate for Lupus
and the flat plateau evident in the right plot of Fig. 8 suggest
that the apparent thickness of Lupus might be the result of different Lupus subclouds being at different distances (see below
Sect. 4.2). Finally, we note that the method proposed here to
study the cloud thickness will certainly provide much more interesting results when a large statistics of high-quality parallaxes
will become available.
4.2. Cloud orientation (tilt)
In order to investigate the presence of possible tilts in the orientation of molecular clouds, we considered a simple model of a
thin cloud located at a distance that is a linear function of the sky
coordinates:
d(x, y) = d0 + d x x + dy y.
(10)
In this equation, d0 is the distance of the cloud at a reference
point (typically, the center of the region considered), and the
150
Distance (pc)
200
Fig. 8. Same as Fig. 7 for Lupus.
4
2
Y tilt
0
60
100
0
-2
-4
-4
-2
0
X tilt
2
4
Fig. 9. A density plot of the derived probability distribution for the tilt
parameters dx and dy of Eq. (10) in Ophiuchus. Similarly to Fig. 7, the
three curves enclose regions of 68%, 95%, and 99.7% confidence level
and the two plots at the top and at the right show the X tilt and Y tilt
marginalized probabilities.
sky coordinates (x, y) are taken to be measured in pc and oriented along the horizontal and vertical axes of Figs. 1 and 2 (so
that d x and dy are pure numbers). This simple prescription can
be directly introduced in Eq. (5) without any further significant
modification of the model.
We studied again this model with MCMC and obtained the
probability distribution for (d x , dy ) shown in Figs. 9 and 10. In
summary, for Ophiuchus we marginally detected a small tilt oriented such that the Ophiuchus streamers would be closer to us
than the ρ Ophiuchi core. Indeed, if we repeat the simple analysis of Sect. 3 to the window marked with a solid line in Fig. 1, the
denser central regions of Ophiuchus that include the well known
ρ Oph core, the distance estimate increases to (128 ± 8) pc. In
contrast, for Lupus we detect a vertical gradient in the distance,
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
where α 1 mag mas. In practice, however, given the relafg
fg
tively large scatter σAV of AV compared to α/π for the cloud
considered in this paper, the effect of the ISM can be safely neglected for the foreground star probability distribution pfg . In
reality, we argue that the same conclusion applies also to the
background distribution pbg . First, we note that the large majority of Hipparcos stars have relatively large parallaxes: for example, in the Ophiucus region we found only 10 objects out of 180
with parallaxes larger than 2 mas. In addition, the combined efbg
bg
fect of a large scatter in σAV of AV and of the filling factor f
makes the detection of a gradient in Abg currently unrealistic. A
specific maximum-likelihood analysis using Eqs. (11) and (12)
has been carried out, and the results show that the arguments just
presented hold. In particular, no significant differences in the distance determinations were found using either a fixed 1 mag mas
or a variable value for α.
We stress, however, that with the advent of GAIA, it will be
possible to apply the method described in this paper to significantly more distant clouds, for which the cumulative effect of
the diffuse ISM can play a relevant role.
8
6
Y tilt
4
2
0
-2
-4
-2
0
2
4
6
X tilt
5. Discussion
Fig. 10. Same as Fig. 9 for Lupus.
with the high-galactic latitude regions at larger distances than the
low-galactic latitude ones (note that, according to the right plot
of Fig. 10, the gradient in galactic latitude is detected at a 3σ
level). Hence, this result together with the large extent of Lupus
on the sky seems to indicate that this complex might not be composed of physically related clouds, as also proposed by Bertout
et al. (1999) and Knude & Nielsen (2001). Unfortunately, in the
current form the method presented here cannot automatically
distinguish multiple components of a cloud complex located at
different distances. Of course, it is always possible to repeat the
analysis in different subclouds, but this requires an a priori assumption on the subcloud division. For Lupus subclouds at high
galactic latitudes, in particular, this is manifestly not viable given
the relatively small number of stars present there. As described
above, we applied this technique to the central region of the
Ophiuchus complex, obtaining a somewhat higher distance for
it. We also considered subregions of Ophiuchus occupying different sectors of Fig. 1 (defined by the two diagonals, the central
vertical line, and the central horizontal line). However, within
the relatively large errors of these analyses, we could not identify any significant difference in the distance. Note that this result
is consistent with large errors shown by the plot of Fig. 9, which
shows that a “flat” screen molecular cloud is still consistent with
our data.
4.3. Effects of diffuse ISM
So far, in our analysis we have implicitly assumed that the only
significant extinction is associated with the molecular cloud.
In reality, the dust present in the interstellar medium (ISM) is
known to produce an average V-band extinction of approximately 1 mag kpc−1 along the galactic plane. In principle, it is
not difficult to take into account this effect by replacing Eqs. (3)
and (4) with
fg
fg2
pfg (AV |π) = Gau(AV |AV + α/π, σAV + σ2AV ),
p (AV ) =
bg
791
bg
Gau(AV |AV
+
bg2
α/π, σAV
+
σ2AV ),
(11)
(12)
Our analysis indicates that the Ophiuchus cloud is very likely to
be closer than the we think: the “standard” distance, 160 pc, is
indeed excluded at 5σ. Not surprisingly, our estimate is in excellent agreement with the one obtained by Knude & Hog (1998)
using a similar technique (but note that the two results are based
on a different datasets and use different statistical methods).
Recently, Wilson (2002) and Mamajek (2007) reported an
Hipparcos estimated distance of Ophiuchus of d = 136+8
−7 pc
pc,
respectively,
results
which
are
marginally
and d = 135+8
−7
in agreement with our distance estimate of the Ophiuchus core.
Mamajek mainly focused on the Lynds 168 cloud, and inferred
the cloud distance from the parallaxes of seven stars presumably associated with illuminated nebulae. Although his method
is plagued by a potential uncertainty, the real association between the Hipparcos stars and the Ophiuchus cloud complex,
and suffers from the small number statistics (7 parallaxes), the
agreement obtained is reassuring and suggests that we finally
have in hand a reliable estimate of the Ophiuchus cloud complex. Wilson (2002), instead, used a more rigorous maximumlikelihood approach, but his analysis is substantially different
from ours. In particular, his method is based on a preliminary
classification of stars as foreground and background based on
their observed reddening; the distance of the cloud is then inferred from the constraints imposed by the parallaxes of the stars
considered. In contrast, in our method we do not need to explicitly classify stars, but on the contrary can use directly all data in
the likelihood (an advantage of this is that we are able to use in
our method also stars that cannot be uniquely classified as foreground or background because, e.g., of their large photometric
errors).
Very recently, Loinard et al. (2008) used phase-referenced
multi-epoch Very Long Baseline Array (VLBA) observations to
measure the trigonometric parallax of the Ophiucus star-forming
region. Their method is based on accurate (to better than a tenth
of a milli-arcsecond), absolute measurements of the position of
individual magnetically active young stars thought to be associated with the star-forming region. If multi-epoch data are available, one can infer the parallax of the star, and thus of the starforming regions, with exquisite accuracy (below 1 pc for objects
within ∼200 pc). This technique was applied to four stars in the
792
M. Lombardi et al.: Hipparcos distances of Ophiuchus and Lupus cloud complexes
ρ-Ophiuchi region, and interestingly it lead to somewhat contradictory results: two objects associated with the sub-condensation
Oph A (S1 and DoAr21) have a measured parallax close to
∼120 pc, and thus in excellent agreement with our estimate; two
others, associated with the condensation Oph B (VSSG14 and
VL5), have a much higher distance of ∼165 pc. A possible explanation of this is provided by a closer examination of the two
sources in the Oph B condensation. From their spectral energy
distributions (SEDs), they appear to be Class III A-type stars,
with little or no circumstellar emitting dust, and an extinction
as large as 50 mag in the V band (see Wilking et al. 1989; and
especially Greene et al. 1994, for a discussion on the individual
SEDs of VSSG14 and VL5). These results indicate that VSSG14
and VL5 are probably background stars, not directly associated
with the Ophiucus complex, and likely to be part of a smaller
OB association at ∼165 pc.
The distance of the Lupus complex is substantially in agreement with the ones reported in the literature, but both the thickness analysis and the orientation analysis suggest noticeable differences in the various Lupus subclouds.
Acknowledgements. We thank Tom Dame and Alex Wilson for useful discussions, and the referee, Jens Knude, for helping us improve the paper with many
useful comments. This research has made use of the 2MASS archive, provided by NASA/IPAC Infrared Science Archive, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This paper also made use of
the Hipparcos and Tycho Catalogs (ESA SP-1200, 1997), the All-sky Compiled
Catalogue of 2.5 million stars (ASCC-2.5, 2001), and the Tycho-2 Spectral Type
Catalog (2003). CJL acknowledges support from NASA ORIGINS Grant NAG
5-13041.
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